Question

use the table to answer the question.

x	$f(x)=12x - 8$
6	64
7	76
8	88

porter is trying to determine how the function $f(x)=12x - 8$ grows. which statement best describes what porter can show using the table?
(1 point)

• the table can be used to show that for $x$-values over equal intervals of 1, the difference between the values of $f(x)$ for the function $y = 12x - 8$ is 52.
• the table can be used to show that for $x$-values over equal intervals of 5, the difference between the values of $f(x)$ for the function $y = 12x - 8$ is 12.
• the table can be used to show that for $x$-values over equal intervals of 1, the difference between the values of $f(x)$ for the function $y = 12x - 8$ is 47.
• the table can be used to show that for $x$-values over equal intervals of 1, the difference in the values of $f(x)$ for the function $y = 12x - 8$ is 12.

Explanation:

Step1: Analyze the x - intervals

The x - values in the table are 5, 6, 7, 8. The interval between consecutive x - values is \(6 - 5=1\), \(7 - 6 = 1\), \(8 - 7=1\). So the x - values are over equal intervals of 1.

Step2: Calculate the differences in f(x) values

• For \(x = 5\), \(f(5)=52\); for \(x = 6\), \(f(6) = 64\). The difference is \(64 - 52=12\).
• For \(x = 6\), \(f(6)=64\); for \(x = 7\), \(f(7)=76\). The difference is \(76 - 64 = 12\).
• For \(x = 7\), \(f(7)=76\); for \(x = 8\), \(f(8)=88\). The difference is \(88 - 76=12\).

So, for x - values over equal intervals of 1, the difference between the values of \(f(x)\) for the function \(y = 12x-8\) is 12.

Answer:

The table can be used to show that for \(x\) - values over equal intervals of 1, the difference in the values of \(f(x)\) for the function \(y = 12x - 8\) is 12. (The corresponding option among the given choices)